There are several types of descriptive measures that can be computed from a set of data (ungrouped or grouped). The three most commonly used are the mean, the median, and the mode.
1. Ungrouped Data
Mean:
Mean is the first and the most commonly measure of central tendency, and it’s determined by adding all the values in population or sample and dividing by the total number of values that are adding.
The population mean is defined by (µ)
µ = ………………… i=1, 2,……, n
The sample mean is defined by ( )
………………………………………… i =1, 2,……, n
The properties of mean are:
1- For a given set of data there is only one mean.
2- Simplicity: is easily understood and easy to compute.
3- Mean is affected by extreme value.
Example: A set data (5, 7, 9, 5, 4).
= = 6
Other set of data with extreme value (5, 7, 9, 5, 24).
= = 10
Median:
The median is that value which located in middle of observations, if these observations are ordered from smallest to largest.
# If the number of observations is even, the median is the average of two middle values.
Example: A set data (10, 54, 10, 33, 21, 53)
Ordered set (10, 10, 21, 33, 53, 54)………….(order the values smallest to largest)
Rank order ( 1, 2, 3, 4, 5, 6)………….(then n=6)
= = = = 27
# If the number of observations is odd, the median is:
Example: A set data (10, 10, 33, 21, 53)
Ordered set (10, 10, 21, 33, 53)…………….(order the values smallest to largest)
Rank order (1, 2, 3, 4, 5)…………….(then n=5)
= = = 21
Mode:
The mode is the value, which occurs most frequency.
Example: (2, 6, 3, 7, 0, 10, 4) ………………………..…………….…………. (No Mode)
(5, 6, 10, 12, 6, 7, 6) ……………………….………………….. (One Mode, 6)
(0, 2, 5, 4, 2, 1, 2, 4, 4) ……………..………………….… (Two Mode, 2, 4)